This video teaches you all about sufficient statistics - what they are, why they're important and useful, and how to find them using the factorization theorem, with examples for the Binomial and Poisson distribution.
I'm glad I found your channel. I have never seen a better explanation of mathematical statistics, nobody else is even close! You are doing an amazing job there
3:04 I love how he describe the indepence of these samples by talking about the coins coming from '3 sets of 10 flips' ... this ensures that the second sample isn't reliant on the first and the third sample isn't reliant on the second and first and so on... in other words, the samples are independent If the samples were taken from a single set of binomial, the probabilty of success of second flip as well as first flip is dependent on success or fail of first sample
To be clear, we are still assuming all the 30 flips are independent and have the same probability of heads - we are just changing how summarize the data. Whether we talking about each flip individually, 3 sets of 10, or 1 set of 30, all 30 coin flips are independent.
Thanks for the video, I'm not grasping only one concept: why is the summation of X_i sufficient in the binomial case (I assume this means we won't need the number of trials)? Shouldn't we know the number of successes with respect to the total trials? For example of course the summation of X_i = 3 where n=5 and where n=100 should give different probabilities
Yes, you're totally correct. We do need to know the number of trials, but that's usually known to us already, so in that case the # of successes is equivalent to the proportion of successes because we can just divide by the (already known) number of trials. (If the number of trials were *also* an unknown parameter that we were trying to learn about, then the number of successes alone would not be sufficient for learning about the probability of success). Let me know if that makes sense or if I can try to clarify further.
